Senate Republicans delivered a blunt warning to President Reagan yesterday that he "should not wait until the 11th hour" to accept a compromise deficit-reduction package, possibly including tax increases, according to administration and congressional sources.

Separately, some Senate Republican leaders said that Social Security, exempt from automatic spending cuts under the new balanced-budget law, nevertheless should be viewed as a target in the search for ways to reduce the deficit.

Senate Majority Leader Robert J. Dole (R-Kan.) said "one of the mistakes we made" last year was to exempt Social Security cost-of-living adjustments from the balanced-budget law, but he said it is "too early to tell" whether Congress will turn to Social Security for deficit savings.

Assistant GOP leader Alan Simpson (R-Wyo.) said, "I think what is going to happen in my mind as we do the Gramm-Rudman-Hollings caper, we're going to find that we left off the table the biggest item, where if we just removed the cost-of-living allowance for a year we could save billions."

Interviewed on the "CBS Morning News," Simpson also said "we've got to revisit" Social Security but later emphasized that he was talking about acting after this year's elections and first round of budget-cutting.

Rep. Leon E. Panetta (D-Calif.) said Social Security should be put on the table for discussion in a deficit compromise. "Nothing can be kept off the table" in light of the cuts needed to meet the $144 billion deficit target mandated for fiscal 1987 by the new law, he said.

Reagan repeated his opposition to any Social Security changes yesterday, Dole said.

On budget strategy, White House officials have said Reagan at the outset will take an uncompromising approach with Congress this year and will seek domestic spending cuts while opposing tax increases or a slowdown in his defense expansion.

Yesterday, the senators, at a White House breakfast, said they understood Reagan's opening stance but had urged him not to remain rigid in March and April when budget votes will be taken.

Sen. Jake Garn (R-Utah) told Reagan that last year's chance to reduce the deficit was wasted, sources said. Other senators said a compromise with Reagan would have to be worked out before the August recess, or else the deep automatic spending cuts in the Gramm-Rudman-Hollings law would almost certainly be triggered.

While the senators did not explicitly urge Reagan to accept a tax increase now, they did ask him to "please recognize that we may have to look at revenues" this year, said a participant in the meeting. Reagan was urged "not to play 'chicken' with the budget," the official said.

Also yesterday, Reagan opened a campaign on behalf of his proposals, to be submitted Feb. 4, to transfer some government functions to the private sector. And he cited pending legislation to sell Conrail, the government-owned rail freight service, to Norfolk Southern.

While Reagan was meeting with GOP senators, House Republican leaders warned yesterday that they want an active role in the budget battle. "We have made it quite clear to the White House that they should not expect to deal with our Senate brethren and then expect us to swallow the line," said House Minority Leader Robert H. Michel (R-Ill.).

"We can make life miserable," said Republican Whip Trent Lott (R-Miss.). "We're going to be a factor. It can be positive or negative."

Lott said he thinks that House Republicans could serve as a "catalyst" in producing a united GOP stance on the budget and deficit issues. While neither he nor Michel would discuss a possible tax increase, both suggested that one would inevitably be part of a deficit compromise.

"As the president's point man in the House, I have to emulate or mirror the president, at least for the moment," Michel said. "But we are headed for some kind of negotiated settlement. Something has got to give."

Lott, judging the mood of his House colleagues, said an oil import fee and higher gasoline taxes appear to be "a very real possibility this year."

House Democrats have announced plans to spotlight what are expected to be massive and politically unpopular domestic spending cuts in Reagan's next budget. As part of that effort, Budget Committee Chairman William H. Gray III (D-Pa.) said his committee will hold hearings on the budget around the country next month. Michel dismissed Gray's plans for crosscountry budget hearings as "a political dog and pony show."

House Speaker Thomas P. (Tip) O'Neill Jr. (D- Mass.) called on Reagan to "put his leadership on the line and tell his Republican supporters that these budget cuts are an essential part of the Reagan program." He said, "These cuts are just a sampler of what is to come. As the budget-cutting parade begins, the president deserves to be grand marshal."

Meanwhile, Sen. Gary Hart (D-Colo.), a prospective Democratic presidential candidate for 1988, called for repeal of Gramm-Rudman-Hollings in favor of a "new contract of cooperation" between Congress and the White House to reduce deficits through tax increases as well as spending cuts.

For the next five years, he suggested savings of roughly $100 billion each from domestic and defense spending projections, coupled with at least $200 billion in tax increases.

In another political maneuver on the budget, Sen. Carl Levin (D-Mich.) released a poll that he said runs counter to Reagan's contention that tax overhaul should be used to cut tax rates rather than to reduce deficits.

Levin said a poll conducted Jan. 10-13 by Opinion Research Corp. of Princeton, N.J., showed twice as much support for reducing deficits as cutting taxes. By a 3-to-1 margin, he said, respondents favored reducing deficits "by billions of dollars" over a $200 average income tax cut from the tax-overhaul bill before Congress.